Just like gold, in fact, during a recession and bank failures Bitcoin may just perform very well, because it has limited quantity, it is decentralized, and it is relatively decorrelating from traditional financial markets.
Lets not compare bitcoin with the way other financial currencies operates, because they are all under different network and technology as well as system, when it comes to the effect of inflation on the market, bitcoin remain unaffected while other fiat currencies are being involved in the reactions towards which the inflation had upon them, that is why we could in most cases see a degradation in market value and currency value as inflation set in.